theorem
  p is closed & X \/ {p} |- q implies X \/ {'not' q} |- 'not' p
proof
  assume that
A1: p is closed and
A2: X \/ {p} |- q;
  X |- p => q by A1,A2,CQC_THE2:92;
  then X |- 'not' q => 'not' p by LUKASI_1:69;
  hence thesis by Th40;
end;
